Examples of vibrating gyroscopes were disclosed by the present applicant in Japanese Patent Disclosure Hei 5-113336 and Japanese Patent Application Hei 6-10348. In these prior circuits, angular velocity is detected by the difference in the currents flowing in two piezo-electric elements having three functions: excitation, detection and feedback.
FIG. 4 illustrates a vibrating gyroscope disclosed in Japanese Patent Application Hei 6-10348. The signal output terminal 9 of drive apparatus 6 is respectively connected to signal input terminals 11L and 11R of feedback amplifiers 10L and 10R having feedback resistances Rf.sub.L and Rf.sub.R. Each of the feedback input terminals 12L and 12R of feedback amplifiers 10L and 10R are connected to one electrode each of piezo-electric elements 2 and 3 that form vibrator 4. The other electrodes of piezo-electric elements 2 and 3 are connected via capacitor Cc to compensation signal output terminal 13 of drive apparatus 6. The compensation signal of the damping capacity of vibrator 4 is outputted at the compensation signal output terminal 13. The signals of the other electrodes of piezo-electric elements 2 and 3 are combined with the compensation signal. The combined signal is amplified at cumulative amplifier 17. Output terminal 18 of the cumulative amplifier 17 is connected to input terminal 14 of the drive apparatus 6, so that vibrator 4 is given self-induced vibration. The outputs of feedback amplifiers 10L and 10R are supplied to differential amplifier 20, so that the Coriolis force arising from the angular velocity acting on vibrator 4 is detected at the output of differential amplifier 20.
Drive apparatus 6, as shown in FIG. 5, has a non-inverting amplifier 15 and an inverting amplifier 16. The signal from input terminal 14 is amplified at non-inverting amplifier 15. The output of non-inverting amplifier 15 is the compensation signal at compensation signal output terminal 13 and is also amplified at inverting amplifier 16 to supply a drive signal to the signal output terminal 9. There is a 180.degree. difference in phase between the drive signal and the compensation signal. The amplitude ratio of these signals is suitably set by inverting amplifier 16.
Examples of the vibrator 4 are shown in FIGS. 6(A) to (F). As shown in FIG. 6(A), the vibrator 4 has a square cross-sectional shape and has piezo-electric element 2 on one side surface 1a of vibration member 1 having a resonance point and piezo-electric element 3 on another side surface 1b adjoining side surface 1a. As shown in FIG. 6(B), the vibrator 4 has piezo-electric elements 2 and 3 split in the wide direction on the same side of vibration member 1. As shown in FIG. 6(C), the vibrator 4 has piezo-electric elements 2 and 3 shifted off center on opposite sides of vibration member 1. As shown in FIG. 6(D), the vibrator 4 has the respective piezo-electric elements 2a and 2b on opposite side surfaces of vibration member 1 and connects them in parallel so that they act essentially as one piezo-electric element 2, while also having the respective piezo-electric elements 3a and 3b on the other opposite sides of vibration member 1 so as to connect them in parallel so that they act essentially as one piezo-electric element 3.
As shown in FIG. 6(E), vibrator 4 has a triangular cross-sectional shape and has piezo-electric elements 2 and 3 on two side surfaces of vibration member 1 having a resonance point. As shown in FIG. 6(F), vibrator 4 has a circular cross-sectional shape and has piezo-electric elements 2 and 3 on the peripheral surface of vibrator member 1 having a resonance point. Thus, members having essentially two piezo-electric elements are formed on the side surfaces of vibration members having various sectional shapes.
With the vibrating gyroscope illustrated in FIG. 4, the imaginary part of the current, relative to the respective damping capacities Cd, flowing in piezo-electric elements 2 and 3 are extinguished by the combined compensation signal flowing through capacitor Cc. Therefore, the output of integrating amplifier 17 becomes only the real part of the current flowing in piezo-electric elements 2 and 3. Consequently, the voltage gain of integrating amplifier 17 maximizes at the mechanical series resonance frequency f.sub.s of vibrator 4, so that vibrator 4 can be stabilized at a frequency in accurate agreement with the mechanical series resonance frequency f.sub.s to give it self-induced vibration.
When angular velocity acts on vibrator 4, a Coriolis force is created and a difference arises between the currents which flow in piezo-electric elements 2 and 5. As a result, there is a difference in the output voltages of the two feedback amplifiers 10L and 10R, so that, for example, by supplying the output of differential amplifier 20 to a synchronous detection circuit and detecting when it is synchronous with the drive signal from drive apparatus 6, it becomes possible to detect the direction and size of the angular velocity.
FIG. 7 illustrates an example of such a synchronous detection circuit. This synchronous detection circuit 25 has a feedback amplifier 26 and a switching element 27, comprising a field-effect type transistor (FET), connected to its non-inverting input terminal. The output of differential amplifier 20 is applied in parallel to the inverting and non-inverting input terminals of differential amplifier 26, while the drive signal from drive apparatus 6 is supplied to the gate terminal of switching element 27. By having the non-inverting input terminal of feedback amplifier 26 synchronized with the drive signal and grounded, it is possible to have synchronous detection of the output of differential amplifier 20.
Also, Japanese Patent Disclosure Sho 62-150116 discloses the detection of angular velocity by sampling and holding of a displacement detection signal by synchronizing to the timing where the appropriate directional component from the circulating drive is at a maximum and a minimum, in a circuit similar to synchronous detection circuit 25 illustrated in FIG. 7.
However, in the conventional synchronous detection circuits as described above, the input signal level does not always necessarily have linear characteristics. For example, when there is a difference in the equivalent resistances of piezo-electric elements 2 and 3, leakage signals that are in-phase or out of phase with the drive signal from drive apparatus 6 are inputted, thereby creating an offset where the direct current level varies, as illustrated in FIG. 8.
On the other hand, taking the periodic external force F (t) as EQU F(t)=F.sub.o cos .omega.t (1)
the displacement x (t) of vibrator 4 becomes ##EQU1## Here, r is the damping constant, m is the equivalent mass, and .omega..sub.o is the mechanical series resonance angular frequency (2.pi.f.sub.s). Also, displacement velocity X (t) shown as a vector is ##EQU2##
Consequently, displacement x(t) of vibrator 4 vibrating at .omega.=.omega..sub.o and displacement velocity X(t) respectively become ##EQU3## where at a time coefficient the same as external force F (t), the times where displacement velocity X(t) is a maximum and a minimum will agree with the times where external force F(t) is maximum and minimum. FIG. 2(A) shows wave form diagrams of the above described F(t), x(t) and X(t).
Similarly, the Coriolis force F.sub.c (t) generated by the applied angular velocity W is shown as ##EQU4## where it goes to a maximum and a minimum at the same times when displacement velocity X(t) is maximum and minimum.
Consequently, when the output of differential amplifier 20 is sampled and held at times when displacement velocity X(t) is at a maximum and a minimum, it becomes theoretically possible to detect the angular velocity.
However, when the currents flowing in a pair of piezo-electric elements 2 and 3 are amplified and fed back to drive apparatus 6, as exemplified in FIG. 4, if we take drive signal v(t) of drive apparatus 6 corresponding to the external force as v(t)=v.sub.o cos .omega.t and the parallel admittances of piezo-electric elements 2 and 3 as Y, then current I(t) flowing in piezo-electric elements 2 and 3 becomes EQU I(t)=Y . v.sub.o cos .omega.t (7)
and, particularly, taking the force coefficient at the mechanical series resonance angular frequency .omega..sub.o as ##EQU5## then the voltage value v.sub.out (t) from integrating amplifier 17 corresponding to the displacement and time differential value of the voltage V.sub.out (t) obtained by its integration and displayed as a vector can be respectively displayed as EQU v.sub.out (t).alpha. cos .omega..sub.o t (8) EQU V.sub.out (t).alpha..omega..sub.o sin .OMEGA..sub.o t (9)
It becomes possible to detect as a signal where the phase is electrically displaced at .pi./2, relative to the actual motion of vibrator 4 shown by formulas (4) and (5) above.
Therefore, even when the output of differential amplifier 20 is sampled and held at a time when displacement velocity X(t) is a maximum and a minimum, the observed value is V.sub.out (t)=0. As a result, the velocity is observed as being zero at such times in terms of electric signals, so that the angular velocity becomes undetectable. Wave form diagrams for the above v(t), v.sub.out (t) and V.sub.out (t) are given in FIG. 2(B).